ya, sometimes pet stores lie. Not always on purpose, sometimes they don't know better, but nope they live a REALLY long time if given the proper living space! My grandma had a pair for almost 40 years!!!!!!!!!! they can live a portion of their life in a small tank like that, but then their insides grow, and their outsides don't so its really painful. (2 gallon bowl with goldfish in it)
Google Image Result for http://pro.corbis.com/images/42-15556213.jpg?size=572&uid=%7BDDE85542-B2E0-4281-B3AB-37F428DA7506%7D they grow pretty large, too. Also, your betta will be ok in his half gallon for now. Just keep up the water changes, and get a larger tank when possible. For bettas a heater is more important that a filter. If the water temp. stays about 76 degrees or above you shouldn't need either tho